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Correlation coefficient is usually used to measure the correlation degree between two time signals. However, its performance will drop or even fail if the signals are noised. Based on the time-frequency phase spectrum (TFPS) provided by normal time-frequency transform (NTFT), similarity coefficient is proposed to measure the similarity between two non-narrow-band time signals, even if the signals are noised. The basic idea of the similarity coefficient is to translate the interest part of signal f1(t)s TFPS along the time axis to couple with signal f2(t)s TFPS. Such coupling would generate a maximum if f1(t)and f2(t) are really similar to each other in time-frequency structure. The maximum, if normalized, is called similarity coefficient. The location of the maximum indicates the time delay between f1(t) and f2(t). Numerical results show that the similarity coefficient is better than the correlation coefficient in measuring the correlation degree between two noised signals. Precision and accuracy of the time delay estimation (TDE) based on the similarity analysis are much better than those based on cross-correlation (CC) method and generalized CC (GCC) method under low SNR.
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Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A simple Gaussian or hyper-Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling. In this paper, we prove that exponential approximation can also be attained for general nonuniform sampling. The analysis is based on the the residue theorem to represent the truncated error by a contour integral. Several concrete examples of nonuniform sampling with exponential convergence will be presented.
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